Chapter 10: Trigonometric Equations

Math 375: Pre-Calculus · LibreTexts

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    From LibreTexts, under CC BY-SA 12, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    • 10.1: The Fundamental Inverse Trigonometric Functions
      This section introduces inverse trigonometric functions, focusing on arcsine, arccosine, and arctangent. It covers their definitions, domains, and ranges, and how to evaluate these functions both exactly and approximately using technology. The section also explores compositions involving trigonometric and inverse trigonometric functions, simplifying expressions, and applying these concepts in modeling and problem-solving.
    • 10.2: The Remaining Inverse Trigonometric Functions
      This section introduces the inverse trigonometric functions for cotangent, secant, and cosecant. It covers their definitions, properties, and domains, along with examples of evaluating these functions exactly and using technology. The section also explains how to simplify compositions and expressions involving these inverse functions, and includes practical exercises to reinforce learning.
    • 10.3: Solving Trigonometric Equations - Algebraic Techniques
      This section focuses on solving trigonometric equations using algebraic techniques. It covers methods for solving basic trigonometric equations, finding solutions using algebraic manipulation, and handling equations with non-standard arguments. The section also includes practical examples, applications, and an algebra refresher to support understanding. Emphasis is placed on identifying all possible solutions, including those in specific intervals.
    • 10.4: Solving Trigonometric Equations Using Identities
      This section focuses on solving trigonometric equations using identities. It discusses strategies for equations involving different trigonometric functions with the same arguments, solving equations with different angular frequencies, and combining trigonometric waves. Practical examples and exercises illustrate how to apply trigonometric identities to simplify and solve complex equations effectively.

    This page titled Chapter 10: Trigonometric Equations was last modified on Tue, 08 Jul 2025 17:46:13 GMT and is shared under a CC BY-SA 12 license and was authored, remixed, and/or curated by Roy Simpson.